(Credits: Some of these materials in this module were adapted from Software Carpentry)
For some, it might just be basic calculations
63.24 * pi # Multiply 63.24 by pi
## [1] 198.6743
exp(x = 4.39) # Raise e to the power of 4.39
## [1] 80.64042
log(x = 1.7) # Take the log of 1.7
## [1] 0.5306283
tan(x = 58) # Compute the tangent of 58
## [1] 8.330857
For others, it might be large or complex mathematical operations
# Take one million samples from the standard normal distribution
data.sample <- rnorm(n = 1000000, mean = 0, sd = 1)
# Build a 1000 x 1000 matrix from the sample data
big.matrix <- matrix(data = data.sample, ncol = 1000)
dim(x = big.matrix) # Confirm that "big.matrix" is 1000 x 1000
## [1] 1000 1000
big.matrix.inverse <- solve(a = big.matrix) # Compute the inverse of "big.matrix"
system.time(expr = solve(a = big.matrix)) # Compute time required to invert "big.matrix"
## user system elapsed
## 0.362 0.294 0.119
It is often said that 80% of data analysis is spent on the process of cleaning and preparing the data. (Dasu and Johnson, 2003)
For most applied researchers, “useful stuff” that can be done in R boils down to a few core items:
For this unit, we'll be working with the “Gapminder” dataset, which is excerpt of the data available at Gapminder.org. For each of 142 countries, the data provides values for life expectancy, GDP per capita, and population, every five years, from 1952 to 2007.
gapminder <- read.csv("../data/gapminder-FiveYearData.csv", stringsAsFactors = TRUE)
head(gapminder)
## country year pop continent lifeExp gdpPercap
## 1 Afghanistan 1952 8425333 Asia 28.801 779.4453
## 2 Afghanistan 1957 9240934 Asia 30.332 820.8530
## 3 Afghanistan 1962 10267083 Asia 31.997 853.1007
## 4 Afghanistan 1967 11537966 Asia 34.020 836.1971
## 5 Afghanistan 1972 13079460 Asia 36.088 739.9811
## 6 Afghanistan 1977 14880372 Asia 38.438 786.1134
So far, you’ve seen the basics of manipulating data frames, e.g. subsetting, merging, and basic calculations. For instance, we can use base R functions to calculate summary statistics across groups of observaitons:
mean(gapminder[gapminder$continent == "Africa", "gdpPercap"])
## [1] 2193.755
mean(gapminder[gapminder$continent == "Americas", "gdpPercap"])
## [1] 7136.11
mean(gapminder[gapminder$continent == "Asia", "gdpPercap"])
## [1] 7902.15
But this isn't ideal because it involves a fair bit of repetition. Repeating yourself will cost you time, both now and later, and potentially introduce some nasty bugs.
Luckily, the dplyr package provides a number of very useful functions for manipulating dataframes. These functions will save you time by reducing repetition. As an added bonus, you might even find the dplyr grammar easier to read.
Here we're going to cover 6 of the most commonly used functions as well as using pipes (%>%) to combine them.
select()filter()group_by()summarize()mutate()arrange()If you have have not installed this package earlier, please do so now:
# not run
# install.packages('dplyr')
Now let's load the package:
library(dplyr)
Imagine that we just received the gapminder dataset, but are only interested in a few variables in it. We could use the select() function to keep only the variables we select.
year_country_gdp <- select(gapminder, year, country, gdpPercap)
head(year_country_gdp)
## year country gdpPercap
## 1 1952 Afghanistan 779.4453
## 2 1957 Afghanistan 820.8530
## 3 1962 Afghanistan 853.1007
## 4 1967 Afghanistan 836.1971
## 5 1972 Afghanistan 739.9811
## 6 1977 Afghanistan 786.1134
If we open up year_country_gdp, we'll see that it only contains the year, country and gdpPercap. This is equivalent to the base R subsetting function:
year_country_gdp <- gapminder[,c("year", "country", "gdpPercap")]
head(year_country_gdp)
## year country gdpPercap
## 1 1952 Afghanistan 779.4453
## 2 1957 Afghanistan 820.8530
## 3 1962 Afghanistan 853.1007
## 4 1967 Afghanistan 836.1971
## 5 1972 Afghanistan 739.9811
## 6 1977 Afghanistan 786.1134
But, as we will see, dplyr makes for much more readible, efficient code because of its pipe operator.
Above, we used what's called 'normal' grammar, but the strengths of dplyr lie in combining several functions using pipes. Since the pipes grammar is unlike anything we've seen in R before, let's repeat what we've done above using pipes.
year_country_gdp <- gapminder %>% select(year,country,gdpPercap)
Let's walk through it step by step. First we summon the gapminder dataframe and pass it on, using the pipe symbol %>%, to the next step, which is the select() function. In this case we don't specify which data object we use in the select() function since in gets that from the previous pipe.
Fun Fact: There is a good chance you have encountered pipes before in the shell. In R, a pipe symbol is %>% while in the shell it is |. But the concept is the same!
Now let's say we're only interested in African countries. We can combine select and filter to select only the observations where continent is Africa.
year_country_gdp_euro <- gapminder %>%
filter(continent == "Africa") %>%
select(year,country,gdpPercap)
As with last time, first we pass the gapminder dataframe to the filter() function, then we pass the filtered version of the gapminder dataframe to the select() function.
To clarify, both the select and filter functions subsets the data frame. The difference is that select extracts certain columns, while filter extracts certain rows.
Note: The order of operations is very important in this case. If we used 'select' first, filter would not be able to find the variable continent since we would have removed it in the previous step.
A common task you'll encounter when working with data is running calculations on different groups within the data. For instance, what if we wanted to calculated the mean GDP per capita for each continent?
In base R, you would have to run the mean() function for each subset of data:
mean(gapminder$gdpPercap[gapminder$continent == "Africa"])
## [1] 2193.755
mean(gapminder$gdpPercap[gapminder$continent == "Americas"])
## [1] 7136.11
mean(gapminder$gdpPercap[gapminder$continent == "Asia"])
## [1] 7902.15
mean(gapminder$gdpPercap[gapminder$continent == "Europe"])
## [1] 14469.48
mean(gapminder$gdpPercap[gapminder$continent == "Oceania"])
## [1] 18621.61
That's a lot of repetition! To make matters worse, what if we wanted to add these values to our original data frame as a new column? We would have to write something like this:
gapminder$mean.continent.GDP <- NA
gapminder$mean.continent.GDP[gapminder$continent == "Africa"] <- mean(gapminder$gdpPercap[gapminder$continent == "Africa"])
gapminder$mean.continent.GDP[gapminder$continent == "Americas"] <- mean(gapminder$gdpPercap[gapminder$continent == "Americas"])
gapminder$mean.continent.GDP[gapminder$continent == "Asia"] <- mean(gapminder$gdpPercap[gapminder$continent == "Asia"])
gapminder$mean.continent.GDP[gapminder$continent == "Europe"] <- mean(gapminder$gdpPercap[gapminder$continent == "Europe"])
gapminder$mean.continent.GDP[gapminder$continent == "Oceania"] <- mean(gapminder$gdpPercap[gapminder$continent == "Oceania"])
You can see how this can get pretty tedious, especially if we want to calculate more complicated or refined statistics. We could use loops or apply functions, but these can be difficult, slow, or error-prone.
The abstract problem we're encountering here is know as “split-apply-combine”:
We want to split our data into groups (in this case continents), apply some calculations on that group, then combine the results together afterwards.
Module 4 gave some ways to do split-apply-combine type stuff using the apply family of functions, but those too are error prone and messy.
Luckily, dplyr offers a much cleaner, straight-forward solution to this problem.
# remove this column -- there's a better way!
gapminder$mean.continent.GDP <- NULL
We've already seen how filter() can help us select observations that meet certain criteria (in the above: continent == "Europe"). More helpful, however, is the group_by() function, which will essentially use every unique criteria that we could have used in filter().
A grouped_df can be thought of as a list where each item in the list is a data.frame which contains only the rows that correspond to the a particular value continent (at least in the example above).
The above was a bit uneventful because group_by() is much more exciting in conjunction with the summarize() function. This will allow use to create new variable(s) by using functions that repeat for each of the continent-specific data frames. In other words, using the group_by() function, we split our original dataframe into multiple pieces, which we then use to run functions (e.g. mean() or sd()) within summarize().
gdp_bycontinents <- gapminder %>%
group_by(continent) %>%
summarize(mean_gdpPercap = mean(gdpPercap))
head(gdp_bycontinents)
## Source: local data frame [5 x 2]
##
## continent mean_gdpPercap
## 1 Africa 2193.755
## 2 Americas 7136.110
## 3 Asia 7902.150
## 4 Europe 14469.476
## 5 Oceania 18621.609
That allowed us to calculate the mean gdpPercap for each continent. But it gets even better – the function group_by() allows us to group by multiple variables. Let's group by year and continent.
gdp_bycontinents_byyear <- gapminder %>%
group_by(continent, year) %>%
summarize(mean_gdpPercap = mean(gdpPercap))
head(gdp_bycontinents_byyear)
## Source: local data frame [6 x 3]
## Groups: continent
##
## continent year mean_gdpPercap
## 1 Africa 1952 1252.572
## 2 Africa 1957 1385.236
## 3 Africa 1962 1598.079
## 4 Africa 1967 2050.364
## 5 Africa 1972 2339.616
## 6 Africa 1977 2585.939
That is already quite powerful, but it gets even better! You're not limited to defining 1 new variable in summarize().
gdp_pop_bycontinents_byyear <- gapminder %>%
group_by(continent, year) %>%
summarize(mean_gdpPercap = mean(gdpPercap),
sd_gdpPercap = sd(gdpPercap),
mean_pop = mean(pop),
sd_pop = sd(pop))
head(gdp_pop_bycontinents_byyear)
## Source: local data frame [6 x 6]
## Groups: continent
##
## continent year mean_gdpPercap sd_gdpPercap mean_pop sd_pop
## 1 Africa 1952 1252.572 982.9521 4570010 6317450
## 2 Africa 1957 1385.236 1134.5089 5093033 7076042
## 3 Africa 1962 1598.079 1461.8392 5702247 7957545
## 4 Africa 1967 2050.364 2847.7176 6447875 8985505
## 5 Africa 1972 2339.616 3286.8539 7305376 10130833
## 6 Africa 1977 2585.939 4142.3987 8328097 11585184
What if we wanted to add these values to our original data frame instead of creating a new object? For this, we can use the mutate() function, which is similar to summarize() except it creates new variables to the same dataframe that you pass into it.
gapminder_with_extra_vars <- gapminder %>%
group_by(continent, year) %>%
mutate(mean_gdpPercap = mean(gdpPercap),
sd_gdpPercap = sd(gdpPercap),
mean_pop = mean(pop),
sd_pop = sd(pop))
head(gapminder_with_extra_vars)
## Source: local data frame [6 x 10]
## Groups: continent, year
##
## country year pop continent lifeExp gdpPercap mean_gdpPercap
## 1 Afghanistan 1952 8425333 Asia 28.801 779.4453 5195.484
## 2 Afghanistan 1957 9240934 Asia 30.332 820.8530 5787.733
## 3 Afghanistan 1962 10267083 Asia 31.997 853.1007 5729.370
## 4 Afghanistan 1967 11537966 Asia 34.020 836.1971 5971.173
## 5 Afghanistan 1972 13079460 Asia 36.088 739.9811 8187.469
## 6 Afghanistan 1977 14880372 Asia 38.438 786.1134 7791.314
## Variables not shown: sd_gdpPercap (dbl), mean_pop (dbl), sd_pop (dbl)
We can use also use mutate() to create new variables prior to (or even after) summarizing information.
gdp_pop_bycontinents_byyear <- gapminder %>%
mutate(gdp_billion = gdpPercap*pop/10^9) %>%
group_by(continent, year) %>%
summarize(mean_gdpPercap = mean(gdpPercap),
sd_gdpPercap = sd(gdpPercap),
mean_pop = mean(pop),
sd_pop = sd(pop),
mean_gdp_billion = mean(gdp_billion),
sd_gdp_billion = sd(gdp_billion))
head(gdp_pop_bycontinents_byyear)
## Source: local data frame [6 x 8]
## Groups: continent
##
## continent year mean_gdpPercap sd_gdpPercap mean_pop sd_pop
## 1 Africa 1952 1252.572 982.9521 4570010 6317450
## 2 Africa 1957 1385.236 1134.5089 5093033 7076042
## 3 Africa 1962 1598.079 1461.8392 5702247 7957545
## 4 Africa 1967 2050.364 2847.7176 6447875 8985505
## 5 Africa 1972 2339.616 3286.8539 7305376 10130833
## 6 Africa 1977 2585.939 4142.3987 8328097 11585184
## Variables not shown: mean_gdp_billion (dbl), sd_gdp_billion (dbl)
As a last step, let's say we want to sort the rows in our data frame according to values in a certain column. We can use the arrange() function to do this. For instance, let's organize our rows by year (recent first), and then by continent.
gapminder_with_extra_vars <- gapminder %>%
group_by(continent, year) %>%
mutate(mean_gdpPercap = mean(gdpPercap),
sd_gdpPercap = sd(gdpPercap),
mean_pop = mean(pop),
sd_pop = sd(pop)) %>%
arrange(desc(year), continent)
head(gapminder_with_extra_vars)
## Source: local data frame [6 x 10]
## Groups: continent, year
##
## country year pop continent lifeExp gdpPercap mean_gdpPercap
## 1 Algeria 1952 9279525 Africa 43.077 2449.0082 1252.572
## 2 Angola 1952 4232095 Africa 30.015 3520.6103 1252.572
## 3 Benin 1952 1738315 Africa 38.223 1062.7522 1252.572
## 4 Botswana 1952 442308 Africa 47.622 851.2411 1252.572
## 5 Burkina Faso 1952 4469979 Africa 31.975 543.2552 1252.572
## 6 Burundi 1952 2445618 Africa 39.031 339.2965 1252.572
## Variables not shown: sd_gdpPercap (dbl), mean_pop (dbl), sd_pop (dbl)
Even before we conduct analysis or calculations, we need to put our data into the correct format. The goal here is to rearrange a messy dataset into one that is tidy
The two most important properties of tidy data are:
1) Each column is a variable. 2) Each row is an observation.
Tidy data is easier to work with, because you have a consistent way of referring to variables (as column names) and observations (as row indices). It then becomes easy to manipulate, visualize, and model.
For more on the concept of tidy data, read Hadley Wickham's paper here
“Tidy datasets are all alike but every messy dataset is messy in its own way.” – Hadley Wickham
Tabular datasets can be arranged in many ways. For instance, consider the data below. Each data set displays information on heart rate observed in individuals across 3 different time periods. But the data are organized differently in each table.
wide <- data.frame(
name = c("Wilbur", "Petunia", "Gregory"),
time1 = c(67, 80, 64),
time2 = c(56, 90, 50),
time3 = c(70, 67, 101)
)
wide
## name time1 time2 time3
## 1 Wilbur 67 56 70
## 2 Petunia 80 90 67
## 3 Gregory 64 50 101
long <- data.frame(
name = c("Wilbur", "Petunia", "Gregory", "Wilbur", "Petunia", "Gregory", "Wilbur", "Petunia", "Gregory"),
time = c(1, 1, 1, 2, 2, 2, 3, 3, 3),
heartrate = c(67, 80, 64, 56, 90, 50, 70, 67, 10)
)
long
## name time heartrate
## 1 Wilbur 1 67
## 2 Petunia 1 80
## 3 Gregory 1 64
## 4 Wilbur 2 56
## 5 Petunia 2 90
## 6 Gregory 2 50
## 7 Wilbur 3 70
## 8 Petunia 3 67
## 9 Gregory 3 10
Question: Which one of these do you think is the tidy format?
Answer: The first dataframe (the “wide” one) would not be considered tidy because values (i.e., heartrate) are spread across multiple columns.
We often refer to these different structurs as “long” vs. “wide” formats. In the “long” format, you usually have 1 column for the observed variable and the other columns are ID variables.
For the “wide” format each row is often a site/subject/patient and you have multiple observation variables containing the same type of data. These can be either repeated observations over time, or observation of multiple variables (or a mix of both). In the above case, we had the same kind of data (heart rate) entered across 3 different columns, corresponding to three different time periods.
You may find data input may be simpler or some other applications may prefer the “wide” format. However, many of R’s functions have been designed assuming you have “long” format data.
Lets look at the structure of our original gapminder dataframe:
head(gapminder)
## country year pop continent lifeExp gdpPercap
## 1 Afghanistan 1952 8425333 Asia 28.801 779.4453
## 2 Afghanistan 1957 9240934 Asia 30.332 820.8530
## 3 Afghanistan 1962 10267083 Asia 31.997 853.1007
## 4 Afghanistan 1967 11537966 Asia 34.020 836.1971
## 5 Afghanistan 1972 13079460 Asia 36.088 739.9811
## 6 Afghanistan 1977 14880372 Asia 38.438 786.1134
Question: Is this data frame wide or long?
Answer: This data frame is somewhere in between the purely 'long' and 'wide' formats. We have 3 “ID variables” (continent, country, year) and 3 “Observation variables” (pop, lifeExp, gdpPercap).
Despite not having ALL observations in 1 column, this intermediate format makes sense given that all 3 observation variables have different units. As we have seen, many of the functions in R are often vector based, and you usually do not want to do mathematical operations on values with different units.
On the other hand, there are some instances in which a purely long or wide format is ideal (e.g. plotting). Likewise, sometimes you'll get data on your desk that is poorly organized, and you'll need to reshape it.
Thankfully, the tidyr package will help you efficiently transform your data regardless of original format.
# Install the "tidyr" package (only necessary one time)
# install.packages("tidyr") # Not Run
# Load the "tidyr" package (necessary every new R session)
library(tidyr)
Until now, we’ve been using the nicely formatted original gapminder dataset. This dataset is not quite wide and not quite long – it's something in the middle, but 'real' data (i.e. our own research data) will never be so well organized. Here let's start with the wide format version of the gapminder dataset.
gap_wide <- read.csv("../data/gapminder_wide.csv", stringsAsFactors = FALSE)
head(gap_wide)
## continent country gdpPercap_1952 gdpPercap_1957 gdpPercap_1962
## 1 Africa Algeria 2449.0082 3013.9760 2550.8169
## 2 Africa Angola 3520.6103 3827.9405 4269.2767
## 3 Africa Benin 1062.7522 959.6011 949.4991
## 4 Africa Botswana 851.2411 918.2325 983.6540
## 5 Africa Burkina Faso 543.2552 617.1835 722.5120
## 6 Africa Burundi 339.2965 379.5646 355.2032
## gdpPercap_1967 gdpPercap_1972 gdpPercap_1977 gdpPercap_1982
## 1 3246.9918 4182.6638 4910.4168 5745.1602
## 2 5522.7764 5473.2880 3008.6474 2756.9537
## 3 1035.8314 1085.7969 1029.1613 1277.8976
## 4 1214.7093 2263.6111 3214.8578 4551.1421
## 5 794.8266 854.7360 743.3870 807.1986
## 6 412.9775 464.0995 556.1033 559.6032
## gdpPercap_1987 gdpPercap_1992 gdpPercap_1997 gdpPercap_2002
## 1 5681.3585 5023.2166 4797.2951 5288.0404
## 2 2430.2083 2627.8457 2277.1409 2773.2873
## 3 1225.8560 1191.2077 1232.9753 1372.8779
## 4 6205.8839 7954.1116 8647.1423 11003.6051
## 5 912.0631 931.7528 946.2950 1037.6452
## 6 621.8188 631.6999 463.1151 446.4035
## gdpPercap_2007 lifeExp_1952 lifeExp_1957 lifeExp_1962 lifeExp_1967
## 1 6223.3675 43.077 45.685 48.303 51.407
## 2 4797.2313 30.015 31.999 34.000 35.985
## 3 1441.2849 38.223 40.358 42.618 44.885
## 4 12569.8518 47.622 49.618 51.520 53.298
## 5 1217.0330 31.975 34.906 37.814 40.697
## 6 430.0707 39.031 40.533 42.045 43.548
## lifeExp_1972 lifeExp_1977 lifeExp_1982 lifeExp_1987 lifeExp_1992
## 1 54.518 58.014 61.368 65.799 67.744
## 2 37.928 39.483 39.942 39.906 40.647
## 3 47.014 49.190 50.904 52.337 53.919
## 4 56.024 59.319 61.484 63.622 62.745
## 5 43.591 46.137 48.122 49.557 50.260
## 6 44.057 45.910 47.471 48.211 44.736
## lifeExp_1997 lifeExp_2002 lifeExp_2007 pop_1952 pop_1957 pop_1962
## 1 69.152 70.994 72.301 9279525 10270856 11000948
## 2 40.963 41.003 42.731 4232095 4561361 4826015
## 3 54.777 54.406 56.728 1738315 1925173 2151895
## 4 52.556 46.634 50.728 442308 474639 512764
## 5 50.324 50.650 52.295 4469979 4713416 4919632
## 6 45.326 47.360 49.580 2445618 2667518 2961915
## pop_1967 pop_1972 pop_1977 pop_1982 pop_1987 pop_1992 pop_1997 pop_2002
## 1 12760499 14760787 17152804 20033753 23254956 26298373 29072015 31287142
## 2 5247469 5894858 6162675 7016384 7874230 8735988 9875024 10866106
## 3 2427334 2761407 3168267 3641603 4243788 4981671 6066080 7026113
## 4 553541 619351 781472 970347 1151184 1342614 1536536 1630347
## 5 5127935 5433886 5889574 6634596 7586551 8878303 10352843 12251209
## 6 3330989 3529983 3834415 4580410 5126023 5809236 6121610 7021078
## pop_2007
## 1 33333216
## 2 12420476
## 3 8078314
## 4 1639131
## 5 14326203
## 6 8390505
The first step towards getting our nice intermediate data format is to first convert from the wide to the long format.
The function gather() will 'gather' the observation variables into a single variable. This is sometimes called “melting” your data, because it melts the table from wide to long. Those data will be melted into two variables: one for the variable names, and the other for the variable values.
gap_long <- gap_wide %>%
gather(obstype_year, obs_values, 3:38)
head(gap_long)
## continent country obstype_year obs_values
## 1 Africa Algeria gdpPercap_1952 2449.0082
## 2 Africa Angola gdpPercap_1952 3520.6103
## 3 Africa Benin gdpPercap_1952 1062.7522
## 4 Africa Botswana gdpPercap_1952 851.2411
## 5 Africa Burkina Faso gdpPercap_1952 543.2552
## 6 Africa Burundi gdpPercap_1952 339.2965
Notice that we put 3 arguments into the gather() function:
obstype_year), obs_value), 3:38, signalling columns 3 through 38) that we want to gather into one variable. Notice that we don't want to melt down columns 1 and 2, as these are considered “ID” variables.We can also select observation variables using:
x:z to select all variables between x and z-y to exclude ystarts_with(x, ignore.case = TRUE): all names that starts with xends_with(x, ignore.case = TRUE): all names that ends with xcontains(x, ignore.case = TRUE): all names that contain xSee the select() function in dplyr for more options.
For instance, here we do the same thing with (1) the starts_with function, and (2) the - operator:
# with the starts_with() function
gap_long <- gap_wide %>%
gather(obstype_year, obs_values, starts_with('pop'),
starts_with('lifeExp'), starts_with('gdpPercap'))
head(gap_long)
## continent country obstype_year obs_values
## 1 Africa Algeria pop_1952 9279525
## 2 Africa Angola pop_1952 4232095
## 3 Africa Benin pop_1952 1738315
## 4 Africa Botswana pop_1952 442308
## 5 Africa Burkina Faso pop_1952 4469979
## 6 Africa Burundi pop_1952 2445618
# with the - operator
gap_long <- gap_wide %>%
gather(obstype_year, obs_values, -continent, -country)
head(gap_long)
## continent country obstype_year obs_values
## 1 Africa Algeria gdpPercap_1952 2449.0082
## 2 Africa Angola gdpPercap_1952 3520.6103
## 3 Africa Benin gdpPercap_1952 1062.7522
## 4 Africa Botswana gdpPercap_1952 851.2411
## 5 Africa Burkina Faso gdpPercap_1952 543.2552
## 6 Africa Burundi gdpPercap_1952 339.2965
However you choose to do it, notice that the output collapses all of the measure variables into two columns: one containing new ID variable, the other containing the observation value for that row.
You'll notice that in our long dataset, obstype_year actually contains 2 pieces of information, the observation type (pop, lifeExp, or gdpPercap) and the year.
We can use the separate() function to split the character strings into multiple variables:
gap_long_sep <- gap_long %>%
separate(obstype_year, into = c('obs_type','year'), sep = "_") %>%
mutate(year = as.integer(year))
head(gap_long_sep)
## continent country obs_type year obs_values
## 1 Africa Algeria gdpPercap 1952 2449.0082
## 2 Africa Angola gdpPercap 1952 3520.6103
## 3 Africa Benin gdpPercap 1952 1062.7522
## 4 Africa Botswana gdpPercap 1952 851.2411
## 5 Africa Burkina Faso gdpPercap 1952 543.2552
## 6 Africa Burundi gdpPercap 1952 339.2965
The opposite of gather() is spread(). It spreads our observation variables back out to make a wider table. We can use this function to spread our gap_long() to the original “medium” format.
gap_medium <- gap_long_sep %>%
spread(obs_type, obs_values)
head(gap_medium)
## continent country year gdpPercap lifeExp pop
## 1 Africa Algeria 1952 2449.008 43.077 9279525
## 2 Africa Algeria 1957 3013.976 45.685 10270856
## 3 Africa Algeria 1962 2550.817 48.303 11000948
## 4 Africa Algeria 1967 3246.992 51.407 12760499
## 5 Africa Algeria 1972 4182.664 54.518 14760787
## 6 Africa Algeria 1977 4910.417 58.014 17152804
All we need is some quick fixes to make this dataset identical to the original gapminder dataset:
gapminder <- read.csv("../data/gapminder-FiveYearData.csv")
head(gap_medium)
## continent country year gdpPercap lifeExp pop
## 1 Africa Algeria 1952 2449.008 43.077 9279525
## 2 Africa Algeria 1957 3013.976 45.685 10270856
## 3 Africa Algeria 1962 2550.817 48.303 11000948
## 4 Africa Algeria 1967 3246.992 51.407 12760499
## 5 Africa Algeria 1972 4182.664 54.518 14760787
## 6 Africa Algeria 1977 4910.417 58.014 17152804
head(gapminder)
## country year pop continent lifeExp gdpPercap
## 1 Afghanistan 1952 8425333 Asia 28.801 779.4453
## 2 Afghanistan 1957 9240934 Asia 30.332 820.8530
## 3 Afghanistan 1962 10267083 Asia 31.997 853.1007
## 4 Afghanistan 1967 11537966 Asia 34.020 836.1971
## 5 Afghanistan 1972 13079460 Asia 36.088 739.9811
## 6 Afghanistan 1977 14880372 Asia 38.438 786.1134
# rearrange columns
gap_medium <- gap_medium[,names(gapminder)]
head(gap_medium)
## country year pop continent lifeExp gdpPercap
## 1 Algeria 1952 9279525 Africa 43.077 2449.008
## 2 Algeria 1957 10270856 Africa 45.685 3013.976
## 3 Algeria 1962 11000948 Africa 48.303 2550.817
## 4 Algeria 1967 12760499 Africa 51.407 3246.992
## 5 Algeria 1972 14760787 Africa 54.518 4182.664
## 6 Algeria 1977 17152804 Africa 58.014 4910.417
# arrange by country, continent, and year
gap_medium <- gap_medium %>%
arrange(country,continent,year)
head(gap_medium)
## country year pop continent lifeExp gdpPercap
## 1 Afghanistan 1952 8425333 Asia 28.801 779.4453
## 2 Afghanistan 1957 9240934 Asia 30.332 820.8530
## 3 Afghanistan 1962 10267083 Asia 31.997 853.1007
## 4 Afghanistan 1967 11537966 Asia 34.020 836.1971
## 5 Afghanistan 1972 13079460 Asia 36.088 739.9811
## 6 Afghanistan 1977 14880372 Asia 38.438 786.1134
dplyr and tiyr have many more functions to help you wrangle and manipulate your data. See the Data Wrangling Cheat Sheet for more.
Once we've carried out group-wise operations and perhaps reshaped it, we may also like to attempt describing the relationships in the data or conducting some causal inference
This often requires doing the following:
Estimating Regressions
Carryingout Regression Diagnostics
Running regressions in R is extremely simple, very straightforwd (though doing things with standard errors requires a little extra work)
Most basic, catch-all regression function in R is glm
glm fits a generalized linear model with your choice of family/link function (gaussian, logit, poisson, etc.)
lm is just a standard linear regression (equivalent to glm with family = gaussian(link = “identity”))
The basic glm call looks something like this:
glm(formula = y~x1+x2+x3+..., family = familyname(link = "linkname"), data = )
There are a bunch of families and links to use (help(family) for a full list), but some essentials are binomial(link = “logit”), gaussian(link = “identity”), and poisson(link = “log”)
Example: suppose we want to regress the life expectency on the GDP per capita and the population, as well as the continent and year. The glm call would be something like this:
# Regress tip percent on total bill and party size
reg <- glm(formula = lifeExp ~ gdpPercap + pop + continent + year,
family = gaussian, data = gapminder)
# View objects contained in the regression output
objects(reg)
## [1] "aic" "boundary" "call"
## [4] "coefficients" "contrasts" "control"
## [7] "converged" "data" "deviance"
## [10] "df.null" "df.residual" "effects"
## [13] "family" "fitted.values" "formula"
## [16] "iter" "linear.predictors" "method"
## [19] "model" "null.deviance" "offset"
## [22] "prior.weights" "qr" "R"
## [25] "rank" "residuals" "terms"
## [28] "weights" "xlevels" "y"
# Examine regression coefficients
reg$coefficients
## (Intercept) gdpPercap pop continentAmericas
## -5.184555e+02 2.984892e-04 1.790640e-09 1.429204e+01
## continentAsia continentEurope continentOceania year
## 9.375486e+00 1.936120e+01 2.055921e+01 2.862583e-01
# Examine regression DoF
reg$df.residual
## [1] 1696
# Examine regression fit (AIC)
reg$aic
## [1] 11420.07
summary(reg)
##
## Call:
## glm(formula = lifeExp ~ gdpPercap + pop + continent + year, family = gaussian,
## data = gapminder)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -28.4051 -4.0550 0.2317 4.5073 20.0217
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.185e+02 1.989e+01 -26.062 <2e-16 ***
## gdpPercap 2.985e-04 2.002e-05 14.908 <2e-16 ***
## pop 1.791e-09 1.634e-09 1.096 0.273
## continentAmericas 1.429e+01 4.946e-01 28.898 <2e-16 ***
## continentAsia 9.375e+00 4.719e-01 19.869 <2e-16 ***
## continentEurope 1.936e+01 5.182e-01 37.361 <2e-16 ***
## continentOceania 2.056e+01 1.469e+00 13.995 <2e-16 ***
## year 2.863e-01 1.006e-02 28.469 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 47.37935)
##
## Null deviance: 284148 on 1703 degrees of freedom
## Residual deviance: 80355 on 1696 degrees of freedom
## AIC: 11420
##
## Number of Fisher Scoring iterations: 2
# Store summary method results
sum.reg <- summary(reg)
# View summary method results objects
objects(sum.reg)
## [1] "aic" "aliased" "call" "coefficients"
## [5] "contrasts" "cov.scaled" "cov.unscaled" "deviance"
## [9] "deviance.resid" "df" "df.null" "df.residual"
## [13] "dispersion" "family" "iter" "null.deviance"
## [17] "terms"
# View table of coefficients
sum.reg$coefficients
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.184555e+02 1.989299e+01 -26.062215 3.248472e-126
## gdpPercap 2.984892e-04 2.002178e-05 14.908225 2.522143e-47
## pop 1.790640e-09 1.634107e-09 1.095791 2.733256e-01
## continentAmericas 1.429204e+01 4.945645e-01 28.898241 1.183161e-149
## continentAsia 9.375486e+00 4.718629e-01 19.869087 3.798275e-79
## continentEurope 1.936120e+01 5.182170e-01 37.361177 2.025551e-223
## continentOceania 2.055921e+01 1.469070e+00 13.994707 3.390781e-42
## year 2.862583e-01 1.005523e-02 28.468586 4.800797e-146
Note that, in our results, R has broken up our variables into their different factor levels (as it will do whenever your regressors have factor levels)
If your data aren't factorized, you can tell glm to factorize a variable (i.e. create dummy variables on the fly) by writing
glm(formula = y~x1+x2+factor(x3), family = family(link = "link"), data = )
x1:x2 interacts all terms in x1 with all terms in x2
summary(glm(formula = lifeExp ~ gdpPercap + pop + continent:factor(year),
family = gaussian, data = gapminder))
##
## Call:
## glm(formula = lifeExp ~ gdpPercap + pop + continent:factor(year),
## family = gaussian, data = gapminder)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -29.5073 -3.4687 0.1739 3.5145 21.1851
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.070e+01 4.745e+00 14.901 < 2e-16
## gdpPercap 3.356e-04 1.997e-05 16.805 < 2e-16
## pop 8.980e-10 1.586e-09 0.566 0.571275
## continentAfrica:factor(year)1952 -3.199e+01 4.831e+00 -6.623 4.77e-11
## continentAmericas:factor(year)1952 -1.881e+01 4.919e+00 -3.823 0.000137
## continentAsia:factor(year)1952 -2.617e+01 4.872e+00 -5.371 8.94e-08
## continentEurope:factor(year)1952 -8.208e+00 4.885e+00 -1.680 0.093146
## continentOceania:factor(year)1952 -4.910e+00 6.668e+00 -0.736 0.461687
## continentAfrica:factor(year)1957 -2.991e+01 4.830e+00 -6.191 7.52e-10
## continentAmericas:factor(year)1957 -1.631e+01 4.918e+00 -3.316 0.000933
## continentAsia:factor(year)1957 -2.337e+01 4.871e+00 -4.797 1.75e-06
## continentEurope:factor(year)1957 -6.351e+00 4.883e+00 -1.301 0.193592
## continentOceania:factor(year)1957 -4.307e+00 6.667e+00 -0.646 0.518393
## continentAfrica:factor(year)1962 -2.793e+01 4.830e+00 -5.782 8.83e-09
## continentAmericas:factor(year)1962 -1.397e+01 4.917e+00 -2.840 0.004564
## continentAsia:factor(year)1962 -2.111e+01 4.871e+00 -4.333 1.56e-05
## continentEurope:factor(year)1962 -4.986e+00 4.880e+00 -1.022 0.307127
## continentOceania:factor(year)1962 -3.886e+00 6.666e+00 -0.583 0.560019
## continentAfrica:factor(year)1967 -2.606e+01 4.829e+00 -5.397 7.75e-08
## continentAmericas:factor(year)1967 -1.221e+01 4.915e+00 -2.484 0.013074
## continentAsia:factor(year)1967 -1.810e+01 4.871e+00 -3.715 0.000210
## continentEurope:factor(year)1967 -4.385e+00 4.877e+00 -0.899 0.368777
## continentOceania:factor(year)1967 -4.265e+00 6.664e+00 -0.640 0.522266
## continentAfrica:factor(year)1972 -2.404e+01 4.828e+00 -4.980 7.03e-07
## continentAmericas:factor(year)1972 -1.051e+01 4.914e+00 -2.138 0.032658
## continentAsia:factor(year)1972 -1.619e+01 4.867e+00 -3.327 0.000899
## continentEurope:factor(year)1972 -4.132e+00 4.874e+00 -0.848 0.396689
## continentOceania:factor(year)1972 -4.311e+00 6.662e+00 -0.647 0.517700
## continentAfrica:factor(year)1977 -2.200e+01 4.828e+00 -4.557 5.58e-06
## continentAmericas:factor(year)1977 -8.800e+00 4.912e+00 -1.791 0.073401
## continentAsia:factor(year)1977 -1.377e+01 4.868e+00 -2.829 0.004722
## continentEurope:factor(year)1977 -3.575e+00 4.871e+00 -0.734 0.463098
## continentOceania:factor(year)1977 -3.657e+00 6.662e+00 -0.549 0.583093
## continentAfrica:factor(year)1982 -1.995e+01 4.828e+00 -4.133 3.77e-05
## continentAmericas:factor(year)1982 -7.017e+00 4.912e+00 -1.428 0.153339
## continentAsia:factor(year)1982 -1.065e+01 4.869e+00 -2.188 0.028825
## continentEurope:factor(year)1982 -3.155e+00 4.870e+00 -0.648 0.517193
## continentOceania:factor(year)1982 -2.649e+00 6.661e+00 -0.398 0.690885
## continentAfrica:factor(year)1987 -1.813e+01 4.828e+00 -3.756 0.000179
## continentAmericas:factor(year)1987 -5.253e+00 4.911e+00 -1.070 0.284987
## continentAsia:factor(year)1987 -8.484e+00 4.869e+00 -1.743 0.081591
## continentEurope:factor(year)1987 -2.855e+00 4.868e+00 -0.587 0.557619
## continentOceania:factor(year)1987 -2.255e+00 6.660e+00 -0.339 0.734934
## continentAfrica:factor(year)1992 -1.785e+01 4.828e+00 -3.697 0.000225
## continentAmericas:factor(year)1992 -3.862e+00 4.911e+00 -0.786 0.431776
## continentAsia:factor(year)1992 -7.151e+00 4.867e+00 -1.469 0.141935
## continentEurope:factor(year)1992 -2.006e+00 4.868e+00 -0.412 0.680292
## continentOceania:factor(year)1992 -7.804e-01 6.659e+00 -0.117 0.906723
## continentAfrica:factor(year)1997 -1.792e+01 4.828e+00 -3.711 0.000213
## continentAmericas:factor(year)1997 -2.565e+00 4.910e+00 -0.522 0.601411
## continentAsia:factor(year)1997 -6.076e+00 4.865e+00 -1.249 0.211930
## continentEurope:factor(year)1997 -1.618e+00 4.866e+00 -0.332 0.739563
## continentOceania:factor(year)1997 -5.865e-01 6.658e+00 -0.088 0.929810
## continentAfrica:factor(year)2002 -1.827e+01 4.827e+00 -3.784 0.000160
## continentAmericas:factor(year)2002 -1.429e+00 4.909e+00 -0.291 0.770984
## continentAsia:factor(year)2002 -4.982e+00 4.865e+00 -1.024 0.305936
## continentEurope:factor(year)2002 -1.307e+00 4.864e+00 -0.269 0.788171
## continentOceania:factor(year)2002 -1.530e-02 6.657e+00 -0.002 0.998167
## continentAfrica:factor(year)2007 -1.695e+01 4.826e+00 -3.512 0.000457
## continentAmericas:factor(year)2007 -8.205e-01 4.906e+00 -0.167 0.867195
## continentAsia:factor(year)2007 -4.265e+00 4.862e+00 -0.877 0.380494
## continentEurope:factor(year)2007 -1.481e+00 4.862e+00 -0.305 0.760680
## continentOceania:factor(year)2007 NA NA NA NA
##
## (Intercept) ***
## gdpPercap ***
## pop
## continentAfrica:factor(year)1952 ***
## continentAmericas:factor(year)1952 ***
## continentAsia:factor(year)1952 ***
## continentEurope:factor(year)1952 .
## continentOceania:factor(year)1952
## continentAfrica:factor(year)1957 ***
## continentAmericas:factor(year)1957 ***
## continentAsia:factor(year)1957 ***
## continentEurope:factor(year)1957
## continentOceania:factor(year)1957
## continentAfrica:factor(year)1962 ***
## continentAmericas:factor(year)1962 **
## continentAsia:factor(year)1962 ***
## continentEurope:factor(year)1962
## continentOceania:factor(year)1962
## continentAfrica:factor(year)1967 ***
## continentAmericas:factor(year)1967 *
## continentAsia:factor(year)1967 ***
## continentEurope:factor(year)1967
## continentOceania:factor(year)1967
## continentAfrica:factor(year)1972 ***
## continentAmericas:factor(year)1972 *
## continentAsia:factor(year)1972 ***
## continentEurope:factor(year)1972
## continentOceania:factor(year)1972
## continentAfrica:factor(year)1977 ***
## continentAmericas:factor(year)1977 .
## continentAsia:factor(year)1977 **
## continentEurope:factor(year)1977
## continentOceania:factor(year)1977
## continentAfrica:factor(year)1982 ***
## continentAmericas:factor(year)1982
## continentAsia:factor(year)1982 *
## continentEurope:factor(year)1982
## continentOceania:factor(year)1982
## continentAfrica:factor(year)1987 ***
## continentAmericas:factor(year)1987
## continentAsia:factor(year)1987 .
## continentEurope:factor(year)1987
## continentOceania:factor(year)1987
## continentAfrica:factor(year)1992 ***
## continentAmericas:factor(year)1992
## continentAsia:factor(year)1992
## continentEurope:factor(year)1992
## continentOceania:factor(year)1992
## continentAfrica:factor(year)1997 ***
## continentAmericas:factor(year)1997
## continentAsia:factor(year)1997
## continentEurope:factor(year)1997
## continentOceania:factor(year)1997
## continentAfrica:factor(year)2002 ***
## continentAmericas:factor(year)2002
## continentAsia:factor(year)2002
## continentEurope:factor(year)2002
## continentOceania:factor(year)2002
## continentAfrica:factor(year)2007 ***
## continentAmericas:factor(year)2007
## continentAsia:factor(year)2007
## continentEurope:factor(year)2007
## continentOceania:factor(year)2007
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 44.3151)
##
## Null deviance: 284148 on 1703 degrees of freedom
## Residual deviance: 72765 on 1642 degrees of freedom
## AIC: 11359
##
## Number of Fisher Scoring iterations: 2
x1*x2 produces the cross of x1 and x2, or x1+x2+x1:x2
summary(glm(formula = lifeExp ~ gdpPercap + pop + continent*factor(year),
family = gaussian, data = gapminder))
##
## Call:
## glm(formula = lifeExp ~ gdpPercap + pop + continent * factor(year),
## family = gaussian, data = gapminder)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -29.5073 -3.4687 0.1739 3.5145 21.1851
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.871e+01 9.235e-01 41.916 < 2e-16
## gdpPercap 3.356e-04 1.997e-05 16.805 < 2e-16
## pop 8.980e-10 1.586e-09 0.566 0.571275
## continentAmericas 1.319e+01 1.621e+00 8.134 8.09e-16
## continentAsia 5.822e+00 1.485e+00 3.920 9.22e-05
## continentEurope 2.379e+01 1.529e+00 15.557 < 2e-16
## continentOceania 2.708e+01 4.800e+00 5.642 1.98e-08
## factor(year)1957 2.086e+00 1.306e+00 1.598 0.110304
## factor(year)1962 4.067e+00 1.306e+00 3.115 0.001871
## factor(year)1967 5.930e+00 1.306e+00 4.542 5.99e-06
## factor(year)1972 7.948e+00 1.306e+00 6.087 1.43e-09
## factor(year)1977 9.994e+00 1.306e+00 7.653 3.32e-14
## factor(year)1982 1.204e+01 1.306e+00 9.221 < 2e-16
## factor(year)1987 1.386e+01 1.306e+00 10.613 < 2e-16
## factor(year)1992 1.414e+01 1.306e+00 10.830 < 2e-16
## factor(year)1997 1.408e+01 1.306e+00 10.779 < 2e-16
## factor(year)2002 1.373e+01 1.306e+00 10.511 < 2e-16
## factor(year)2007 1.504e+01 1.306e+00 11.515 < 2e-16
## continentAmericas:factor(year)1957 4.129e-01 2.291e+00 0.180 0.857023
## continentAsia:factor(year)1957 7.150e-01 2.095e+00 0.341 0.732979
## continentEurope:factor(year)1957 -2.288e-01 2.159e+00 -0.106 0.915582
## continentOceania:factor(year)1957 -1.483e+00 6.784e+00 -0.219 0.826997
## continentAmericas:factor(year)1962 7.727e-01 2.291e+00 0.337 0.735962
## continentAsia:factor(year)1962 9.945e-01 2.095e+00 0.475 0.635119
## continentEurope:factor(year)1962 -8.452e-01 2.159e+00 -0.391 0.695499
## continentOceania:factor(year)1962 -3.043e+00 6.784e+00 -0.449 0.653798
## continentAmericas:factor(year)1967 6.632e-01 2.291e+00 0.289 0.772261
## continentAsia:factor(year)1967 2.145e+00 2.095e+00 1.024 0.306043
## continentEurope:factor(year)1967 -2.107e+00 2.160e+00 -0.976 0.329424
## continentOceania:factor(year)1967 -5.285e+00 6.784e+00 -0.779 0.436082
## continentAmericas:factor(year)1972 3.507e-01 2.291e+00 0.153 0.878376
## continentAsia:factor(year)1972 2.032e+00 2.096e+00 0.969 0.332439
## continentEurope:factor(year)1972 -3.873e+00 2.161e+00 -1.792 0.073375
## continentOceania:factor(year)1972 -7.349e+00 6.785e+00 -1.083 0.278856
## continentAmericas:factor(year)1977 1.084e-02 2.292e+00 0.005 0.996226
## continentAsia:factor(year)1977 2.404e+00 2.096e+00 1.147 0.251547
## continentEurope:factor(year)1977 -5.362e+00 2.163e+00 -2.478 0.013293
## continentOceania:factor(year)1977 -8.742e+00 6.785e+00 -1.288 0.197779
## continentAmericas:factor(year)1982 -2.520e-01 2.292e+00 -0.110 0.912450
## continentAsia:factor(year)1982 3.479e+00 2.096e+00 1.660 0.097163
## continentEurope:factor(year)1982 -6.988e+00 2.165e+00 -3.227 0.001276
## continentOceania:factor(year)1982 -9.780e+00 6.785e+00 -1.441 0.149674
## continentAmericas:factor(year)1987 -3.056e-01 2.292e+00 -0.133 0.893940
## continentAsia:factor(year)1987 3.829e+00 2.096e+00 1.827 0.067953
## continentEurope:factor(year)1987 -8.505e+00 2.169e+00 -3.922 9.14e-05
## continentOceania:factor(year)1987 -1.120e+01 6.786e+00 -1.651 0.098952
## continentAmericas:factor(year)1992 8.020e-01 2.292e+00 0.350 0.726462
## continentAsia:factor(year)1992 4.878e+00 2.097e+00 2.326 0.020134
## continentEurope:factor(year)1992 -7.940e+00 2.168e+00 -3.662 0.000258
## continentOceania:factor(year)1992 -1.001e+01 6.786e+00 -1.475 0.140318
## continentAmericas:factor(year)1997 2.164e+00 2.292e+00 0.944 0.345341
## continentAsia:factor(year)1997 6.019e+00 2.098e+00 2.869 0.004174
## continentEurope:factor(year)1997 -7.487e+00 2.172e+00 -3.446 0.000582
## continentOceania:factor(year)1997 -9.753e+00 6.788e+00 -1.437 0.150990
## continentAmericas:factor(year)2002 3.649e+00 2.293e+00 1.591 0.111701
## continentAsia:factor(year)2002 7.461e+00 2.099e+00 3.555 0.000388
## continentEurope:factor(year)2002 -6.827e+00 2.178e+00 -3.134 0.001753
## continentOceania:factor(year)2002 -8.833e+00 6.791e+00 -1.301 0.193515
## continentAmericas:factor(year)2007 2.942e+00 2.294e+00 1.283 0.199720
## continentAsia:factor(year)2007 6.864e+00 2.101e+00 3.267 0.001108
## continentEurope:factor(year)2007 -8.316e+00 2.187e+00 -3.803 0.000148
## continentOceania:factor(year)2007 -1.013e+01 6.793e+00 -1.492 0.135983
##
## (Intercept) ***
## gdpPercap ***
## pop
## continentAmericas ***
## continentAsia ***
## continentEurope ***
## continentOceania ***
## factor(year)1957
## factor(year)1962 **
## factor(year)1967 ***
## factor(year)1972 ***
## factor(year)1977 ***
## factor(year)1982 ***
## factor(year)1987 ***
## factor(year)1992 ***
## factor(year)1997 ***
## factor(year)2002 ***
## factor(year)2007 ***
## continentAmericas:factor(year)1957
## continentAsia:factor(year)1957
## continentEurope:factor(year)1957
## continentOceania:factor(year)1957
## continentAmericas:factor(year)1962
## continentAsia:factor(year)1962
## continentEurope:factor(year)1962
## continentOceania:factor(year)1962
## continentAmericas:factor(year)1967
## continentAsia:factor(year)1967
## continentEurope:factor(year)1967
## continentOceania:factor(year)1967
## continentAmericas:factor(year)1972
## continentAsia:factor(year)1972
## continentEurope:factor(year)1972 .
## continentOceania:factor(year)1972
## continentAmericas:factor(year)1977
## continentAsia:factor(year)1977
## continentEurope:factor(year)1977 *
## continentOceania:factor(year)1977
## continentAmericas:factor(year)1982
## continentAsia:factor(year)1982 .
## continentEurope:factor(year)1982 **
## continentOceania:factor(year)1982
## continentAmericas:factor(year)1987
## continentAsia:factor(year)1987 .
## continentEurope:factor(year)1987 ***
## continentOceania:factor(year)1987 .
## continentAmericas:factor(year)1992
## continentAsia:factor(year)1992 *
## continentEurope:factor(year)1992 ***
## continentOceania:factor(year)1992
## continentAmericas:factor(year)1997
## continentAsia:factor(year)1997 **
## continentEurope:factor(year)1997 ***
## continentOceania:factor(year)1997
## continentAmericas:factor(year)2002
## continentAsia:factor(year)2002 ***
## continentEurope:factor(year)2002 **
## continentOceania:factor(year)2002
## continentAmericas:factor(year)2007
## continentAsia:factor(year)2007 **
## continentEurope:factor(year)2007 ***
## continentOceania:factor(year)2007
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 44.3151)
##
## Null deviance: 284148 on 1703 degrees of freedom
## Residual deviance: 72765 on 1642 degrees of freedom
## AIC: 11359
##
## Number of Fisher Scoring iterations: 2
The package lmtest has most of what you'll need to run basic regression diagnostics.
Breusch-Pagan Test for Heteroscedasticity
bptest(reg)
##
## studentized Breusch-Pagan test
##
## data: reg
## BP = 174.08, df = 7, p-value < 2.2e-16
bgtest(reg)
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: reg
## LM test = 1241.4, df = 1, p-value < 2.2e-16
dwtest(reg)
##
## Durbin-Watson test
##
## data: reg
## DW = 0.29392, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
coeftest(x = reg, vcov. = vcovHC)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.1846e+02 2.5634e+01 -20.2249 < 2.2e-16 ***
## gdpPercap 2.9849e-04 4.8328e-05 6.1763 6.561e-10 ***
## pop 1.7906e-09 1.3057e-09 1.3714 0.1703
## continentAmericas 1.4292e+01 5.2624e-01 27.1588 < 2.2e-16 ***
## continentAsia 9.3755e+00 5.6555e-01 16.5776 < 2.2e-16 ***
## continentEurope 1.9361e+01 6.9851e-01 27.7177 < 2.2e-16 ***
## continentOceania 2.0559e+01 1.0739e+00 19.1441 < 2.2e-16 ***
## year 2.8626e-01 1.3013e-02 21.9982 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Use dplyr to create a data frame containing the median lifeExp for each continent
Use dplyr to add a column to the gapminder dataset that contains the total population of the continent of each observation in a given year. For example, if the first observation is Afghanistan in 1952, the new column would contain the population of Asia in 1952.
Use dplyr to: add a column called gdpPercap_diff that contains the difference between the observation's gdpPercap and the mean gdpPercap of the continent in that year. Arrange the dataframe by the column you just created, in descending order (so that the relatively richest country/years are listed first)
hint: You might have to ungoup() before you arrange().
country, year, and gdpPercap_diff columns. Use tidyr put it in wide format so that countries are rows and years are columns. Fit two linear regression models from the gapminder data, where the outcome is gdpPercap and the explanatory variables are pop, lifeExp, and year. In one model, treat year as a numeric variable. In the other, factorize the year variable. How do you interpret each model?
Fix a logit model where the outcome is whether gdpPercap_diff is positive or negative – that is, whether an observation is in the upper half or lower half of the continent's wealth in a given year. The explanatory variables should be country, lifeExp, and pop.